Moreover, in the setting of NIP theories (a class that includes dp-minimal theories), the Alon-Kleitman-Matoušek \((p,q)\) -theorem [1]} implies the following. Any definable family of sets in an NIP structure with the \((p,q)\) -property (the property that, for every \(p\)  sets in the family, some \(q\)  intersect), for some \(p\ge q\)  with \(q\)  large enough (i.e. \(q\)  greater than the \(\text{VC}\) -codensity of the family), admits a partition into finitely many consistent subfamilies. The definable \((p,q)\) -conjecture of Simon [2]} states that these subfamilies can be chosen to be definable (see [3]} for recent work in this direction).
